Basic Math Examples

$\frac{7}{\sqrt{11} - 2}$

Step 1

Multiply $\frac{7}{\sqrt{11} - 2}$ by $\frac{\sqrt{11} + 2}{\sqrt{11} + 2}$ .

$\frac{7}{\sqrt{11} - 2} \cdot \frac{\sqrt{11} + 2}{\sqrt{11} + 2}$

Step 2

Multiply $\frac{7}{\sqrt{11} - 2}$ by $\frac{\sqrt{11} + 2}{\sqrt{11} + 2}$ .

$\frac{7 (\sqrt{11} + 2)}{(\sqrt{11} - 2) (\sqrt{11} + 2)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (\sqrt{11} + 2)}{{\sqrt{11}}^{2} + \sqrt{11} \cdot 2 - 2 \sqrt{11} - 4}$

Step 4

Simplify.

$\frac{7 (\sqrt{11} + 2)}{7}$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Cancel the common factor.

$\frac{7 (\sqrt{11} + 2)}{7}$

Step 5.2

Divide $\sqrt{11} + 2$ by $1$ .

$\sqrt{11} + 2$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{11} + 2$

Decimal Form:

$5.31662479 \dots$